1. Field of the Invention
The invention relates to a projection method of three-dimensional imaging, and more particularly to the projection method of three-dimensional imaging applied to the field of the radiological medicine.
2. Description of the Prior Art
As the technology progresses, imaging in the radiological medicine has become an effective diagnostic tool. The imaging is executed firstly by building an appropriate numerical model that satisfies the related physical phenomena, and then by reconstructing a relevant three-dimensional (3D) image through image-reconstruction algorithms. Popular imaging methods nowadays include the computed tomography (CT), the positron emission tomography (PET), the single-photon emission computed tomography (SPECT) and the like.
In the history of image-reconstruction algorithms, early analytical methods include the filtered back projection (FBP), the matrix inversion tomosynthesis (MITS) and so on. Recently, as the rapid development in computer and hardware technology, the iterative techniques for achieving high-resolution imaging quality such as the maximum likelihood expectation maximization (MLEM), the ordered subset expectation maximization (OSEM), the algebraic reconstruction technique (ART), the projection onto convex sets (POCS) and the like re-construction algorithms become the mainstream. However, in order to obtain further better imaging quality, more precise systematic matrix models shall be introduced for the calculations of the iterative reconstruction.
By having the computed tomography for example, the imaging device receives signals and then transfers the signals into a discrete matrix. The discrete matrix that is then stored in the computer as a mathematic model for image reconstruction can be expressed as follows.[G]m×n[f]n×1=[C]m×1 
where vector C (m×1) is the received signal in a discrete form stored in the computer, matrix G is the system matrix (m×n), and vector f(n×1) is the 3D image to be solved. Knowing that the photon travels straightly and neglecting other physical factors such as scattering, it is assumed that an imaging device can receive signals and emit a volume source detectable by a detector. Under such a circumstance, the aforesaid G can be simplified as a matrix depicting the geometric relationship, where gij stands for the geometric detection effect of the i-th voxel with respect to the j-th detector. For the detectors are disposed at different positions, the received signals would be different in a possibility view. Thus, the possibility information shall be fed back to the reconstruction process so as to amend the difference in spatial distribution.
In the foregoing equation, the computation of a big matrix is time-consuming and thus forms a bottleneck. For example, if the f is a 512×512×512 3D image having n=134217728 image pixels and apply a 3072×3072 detector to perform a 360-degree imaging by a sampling rate of each 1 degree increment., then m=3072×3072×360 and the matrix dimension would be 3397386240×134217728˜4.56e+17. Limited by the computation resources of the computer, the question of how to precisely depict the system and how to apply the concept of the sparse matrix to reduce the calculation time of the computer has become a challenge in applications of the iterative reconstruction.
In current art, the ray tracing is usually applied to resolve the aforesaid question. Further, a program optimization application is proposed by Siddon R L (1985). Therefore, various image-processing techniques based on the ray tracing are now developing, such as the technique to simulate the travelling trace of the photon in a defined space, the technique to investigate the crystal penetrability and so on. By having the computed tomography as an example, where the light source and the detector are assumed to be volume-less, and the center of light source and the center of the detector are defined as two fixed points. Through the light-beam connection between these two fixed points to depict the imaging, the possibility is defined to be the length of the light beam that crosses the voxels of the image in the space, and the gij for image reconstruction is defined as the ratio of the length of a light beam passing the voxel to the length of the whole imaging space. It is clear that the effect on the imaging by the volumes of the light source and the detector has been overlooked. Also, in order to obtain higher resolution, when the voxel is smaller than a detector in volume, the effect of the voxel on the imaging might be neglected. To have this problem be resolved, a means of increasing the number of the light beams can be applied; namely, by segmenting the mathematic model of the detector further so as to reduce the effect of the detector's volume upon the calculation. For example, in a document of Huesman R H (2000), each of the two detection units is cut into 3×3 so as to increase the total number of the light beams to 729 times (for the light beams are received by pairs). Though the slope and the ratio of the light beams can be compressed and simplified, yet the improvement therefrom is a trade-off subjected to the O(n4) algorithm. Therefore, the ray tracing pattern may simplify the model and have advantages in calculation, yet the requirements in more sub-rays for reconstructing and more computation time for increasing the imaging precision would form a barrier to inhibit its practice.
In addition, another resort thereof is to assume the voxel into a sphere. A typical name for such a resort is the spherically symmetric volume elements (blobs). By adopting relevant mathematical equations and applying the distance between a point to the spherical center, the density inside the sphere can be adjusted. This technical resort is usually applied to an imaging process that needs a higher resolution. For example, in an article by Marabini R L (1998), this resort is applied to an electron microscope. Nevertheless, the computation time related to this resort would be huge, and thus the application thereof can be seen in the academic research or in the simulation, but seldom in the industry.
Commercially, a popular method uses the ray tracing technique in cooperating with the interpolation. This improved technique is also called as a ray driven or pixel driven technique. In this resort, a weighting rearrangement has been processed through an interpolating consideration in distances, from which no more data loss in compressing the z-directional information caused by neglecting any voxel in the concerned space would happen. (It is well known that the aforesaid data loss will lead to more bias for imaging under a larger angle.)
To meet the precision requirement in image reconstruction and to avoid cost hike in calculation of time-consuming iterative reconstruction, the analytical methods are usually the inevitable choices in the current marketplace. Hence, the need for developing a new model-based iterative reconstruction algorithm can be foreseen, such as a clustering algorithm for footprints or a parallel accelerating algorithm. Nowadays, some major medical manufacturers also invest money on developing new techniques for the iterative reconstruction method and try to develop a more precise model for researching the iterative reconstruction techniques, so as hopefully to obtain a 3D reconstructed image with a higher resolution but without huge calculations.